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</div>		<h1 id="firstHeading" class="firstHeading"><span><span>Kasiski examination</span></span></h1>
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<td class="mbox-text" style="">This article <b>needs additional <a href="http://en.wikipedia.org/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">citations</a> for <a href="http://en.wikipedia.org/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a>.</b> Please help <a href="http://en.wikipedia.org/w/index.php?title=Kasiski_examination&amp;action=edit" class="external text" title="http://en.wikipedia.org/w/index.php?title=Kasiski_examination&amp;action=edit" rel="nofollow">improve this article</a> by adding <a href="http://en.wikipedia.org/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">reliable references</a> (ideally, using <i><a href="http://en.wikipedia.org/wiki/Wikipedia:Footnotes" title="Wikipedia:Footnotes">inline citations</a></i>). Unsourced material may be <a href="http://en.wikipedia.org/wiki/Template:Fact" title="Template:Fact">challenged</a> and <a href="http://en.wikipedia.org/wiki/Wikipedia:BURDEN" title="Wikipedia:BURDEN" class="mw-redirect">removed</a>. <small><i>(March 2009)</i></small></td>
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<p>In <a href="http://en.wikipedia.org/wiki/Cryptanalysis" title="Cryptanalysis">cryptanalysis</a>, <strong class="selflink">Kasiski examination</strong> (also referred to as <b>Kasiski's Test</b> or <b>Kasiski's Method</b>) is a method of attacking <a href="http://en.wikipedia.org/wiki/Polyalphabetic_cipher" title="Polyalphabetic cipher">polyalphabetic substitution ciphers</a>, such as the <a href="http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" title="Vigenère cipher">Vigenère cipher</a>. It was first published by <a href="http://en.wikipedia.org/wiki/Friedrich_Kasiski" title="Friedrich Kasiski">Friedrich Kasiski</a> in 1863<sup id="cite_ref-0" class="reference"><a href="#cite_note-0" title=""><span>[</span>1<span>]</span></a></sup>, but seems to have been independently discovered by <a href="http://en.wikipedia.org/wiki/Charles_Babbage" title="Charles Babbage">Charles Babbage</a> as early as 1846<sup id="cite_ref-1" class="reference"><a href="#cite_note-1" title=""><span>[</span>2<span>]</span></a></sup>.</p>
<table id="toc" class="toc" summary="Contents">
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<td>
<div id="toctitle">
<h2>Contents</h2>
 <span class="toctoggle">[<a href="javascript:toggleToc()" class="internal" id="togglelink">hide</a>]</span></div>
<ul>
<li class="toclevel-1"><a href="#How_it_works"><span class="tocnumber">1</span> <span class="toctext">How it works</span></a></li>
<li class="toclevel-1"><a href="#A_string_based_attack"><span class="tocnumber">2</span> <span class="toctext">A string based attack</span></a></li>
<li class="toclevel-1"><a href="#Superposition"><span class="tocnumber">3</span> <span class="toctext">Superposition</span></a></li>
<li class="toclevel-1"><a href="#References"><span class="tocnumber">4</span> <span class="toctext">References</span></a></li>
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<p><a name="How_it_works" id="How_it_works"></a></p>
<h2><span class="editsection">[<a href="http://en.wikipedia.org/w/index.php?title=Kasiski_examination&amp;action=edit&amp;section=1" title="Edit section: How it works">edit</a>]</span> <span class="mw-headline">How it works</span></h2>
<p>The Kasiski examination allows a cryptanalyst to deduce the length
of the keyword used in the polyalphabetic substitution cipher. Once the
length of the keyword is discovered, the cryptanalyst lines up the
ciphertext in <i>n</i> columns, where <i>n</i> is the length of the keyword. Then, each column can be treated as the ciphertext of a <a href="http://en.wikipedia.org/wiki/Monoalphabetic_substitution_cipher" title="Monoalphabetic substitution cipher" class="mw-redirect">monoalphabetic substitution cipher</a>. As such, each column can be attacked with <a href="http://en.wikipedia.org/wiki/Frequency_analysis" title="Frequency analysis">frequency analysis</a>.</p>
<p>The Kasiski examination involves looking for strings of characters that are repeated in the <a href="http://en.wikipedia.org/wiki/Ciphertext" title="Ciphertext" class="mw-redirect">ciphertext</a>.
The strings should be three characters long or more for the examination
to be successful. Then, the distances between consecutive occurrences
of the strings are likely to be multiples of the length of the keyword.
Thus finding more repeated strings narrows down the possible lengths of
the keyword, since we can take the <a href="http://en.wikipedia.org/wiki/Greatest_common_divisor" title="Greatest common divisor">greatest common divisor</a> of all the distances.</p>
<p>The reason this test works is that if a repeated string occurs in the <a href="http://en.wikipedia.org/wiki/Plaintext" title="Plaintext">plaintext</a>,
and the distance between them is a multiple of the keyword length, the
keyword letters will line up in the same way with both occurrences of
the string. For example, consider the plaintext:</p>
<pre>crypto is short for cryptography.
</pre>
<p>"<tt>crypto</tt>" is a repeated string, and the distance between the
occurrences is 20 characters. We will line up the plaintext with first
a six-character keyword "<tt>abcdef</tt>" (6 does not divide 20) and a five-character keyword "<tt>abcde</tt>" (5 divides 20).</p>
<pre><b>abcdef</b>abcdefabcdefab<b>cdefab</b>cdefabc
<b>crypto</b> is short for <b>crypto</b>graphy.
</pre>
<p>Notice that the first instance of "<tt>crypto</tt>" lines up with "<tt>abcdef</tt>" and the second instance lines up with "<tt>cdefab</tt>". The two instances will encrypt to different ciphertexts.</p>
<pre><b>abcdea</b>bcdeabcdeabcde<b>abcdea</b>bcdeabc
<b>crypto</b> is short for <b>crypto</b>graphy.
</pre>
<p>Note that both occurrences of "<tt>crypto</tt>" now line up with "<tt>abcdea</tt>". The two instances will encrypt to the same ciphertext and the Kasiski examination will be effective.</p>
<p><a name="A_string_based_attack" id="A_string_based_attack"></a></p>
<h2><span class="editsection">[<a href="http://en.wikipedia.org/w/index.php?title=Kasiski_examination&amp;action=edit&amp;section=2" title="Edit section: A string based attack">edit</a>]</span> <span class="mw-headline">A string based attack</span></h2>
<p>The difficulty of using the Kasiski examination lies in finding
repeated strings. This is a very hard task to perform manually, but
computers can make it much easier. However, human interaction is still
required, since some repeated strings may just be coincidence, and the
distances will have a greatest common divisor of 1. A human
cryptanalyst has to rule out the coincidences to find the correct
length. Then, of course, the human has to cryptanalyze the
monoalphabetic ciphertexts that result.</p>
<ol>
<li>A cryptanalyst looks for repeated groups of letters and counts the
number of letters between the beginning of each repeated group. For
instance if the ciphertext was <tt><b>FGX</b>THJAQWN<b>FGX</b>Q</tt>, the distance between <tt>FGX</tt>'s is 10. The analyst repeats this for as many repeated groups as appear in the text.</li>
<li>The analyst next <a href="http://en.wikipedia.org/wiki/Integer_factorisation" title="Integer factorisation" class="mw-redirect">factors</a>
each of these numbers. If any number is repeated in the majority of
these factorings, this is probably the length of the keyword. This is
because repeated groups can appear by coincidence, but are much more
likely to occur when the same letters are encrypted using the same key
letters. The key letters are repeated at multiples of the key length,
so the distances found in step 1 are likely to be multiples of the key
length.</li>
<li>Once the keyword length is known, the clever observation of Babbage and Kasiski comes into play. If the keyword is <var>N</var> letters long, then every <var>N</var>th letter must have been enciphered using the same letter of the keytext. Grouping every <var>N</var>th letter together, the analyst has <var>N</var> "messages", each encrypted using a one-alphabet substitution, and each piece can then be solved using frequency analysis.</li>
<li>Using the solved message, the analyst can quickly determine what
the keyword was. Or, in the process of solving the pieces, the analyst
might use guesses about the keyword to assist in breaking the message.</li>
<li>Once the interceptor knows the keyword, he or she can use that knowledge to read future messages, if the key does not change.</li>
</ol>
<p><a name="Superposition" id="Superposition"></a></p>
<h2><span class="editsection">[<a href="http://en.wikipedia.org/w/index.php?title=Kasiski_examination&amp;action=edit&amp;section=3" title="Edit section: Superposition">edit</a>]</span> <span class="mw-headline">Superposition</span></h2>
<p>Kasiski actually used "superimposition" to solve the Vigenère
cipher. He started by finding the key length, as above. Then he took
multiple copies of the message and laid them one-above-another, each
one shifted left by the length of the key. Kasiski then observed that
each <i>column</i> was made up of letters encrypted with a single
alphabet. His method was equivalent to the one described above, but is
perhaps easier to picture.</p>
<p>Modern attacks on polyalphabetic ciphers are essentially identical to that described above, with the one improvement of <a href="http://en.wikipedia.org/wiki/Coincidence_counting" title="Coincidence counting" class="mw-redirect">coincidence counting</a>. Instead of looking for repeating groups, a modern analyst would take two copies of the message and lay one above another.</p>
<p>Modern analysts use computers, but this description illustrates the principle that the computer algorithms implement.</p>
<p>The generalized method</p>
<ol>
<li>The analyst then shifts the bottom message one letter to the left,
then two letters to the left, etc., each time going through the entire
message and counting the number of times the same letter appears in the
top and bottom message.</li>
<li>The number of "coincidences" goes up sharply when the bottom
message is shifted by a multiple of the key length, because then the
adjacent letters are in the same language using the same alphabet.</li>
<li>Having found the key length, cryptanalysis proceeds as described above using frequency analysis.</li>
</ol>
<p><a name="References" id="References"></a></p>
<h1><span class="editsection">[<a href="http://en.wikipedia.org/w/index.php?title=Kasiski_examination&amp;action=edit&amp;section=4" title="Edit section: References">edit</a>]</span> <span class="mw-headline">References</span></h1>
<div class="references-small">
<ol class="references">
<li id="cite_note-0"><b><a href="#cite_ref-0" title="">^</a></b> Kasiski, F. W. 1863. Die Geheimschriften und die Dechiffrir-Kunst. Berlin: E. S. Mittler und Sohn</li>
<li id="cite_note-1"><b><a href="#cite_ref-1" title="">^</a></b> Franksen, O. I. 1985 Mr. Babbage's Secret: the Tale of a Cipher-And APL. Prentice Hall</li>
</ol>
</div>
<p><br></p>
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<p><span style="white-space: nowrap;"><b>Ciphers:</b> <a href="http://en.wikipedia.org/wiki/ADFGVX_cipher" title="ADFGVX cipher">ADFGVX</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Affine_cipher" title="Affine cipher">Affine</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Alberti_cipher" title="Alberti cipher">Alberti</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Atbash" title="Atbash">Atbash</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Autokey_cipher" title="Autokey cipher">Autokey</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Bifid_cipher" title="Bifid cipher">Bifid</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Book_cipher" title="Book cipher">Book</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Caesar_cipher" title="Caesar cipher">Caesar</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Four-square_cipher" title="Four-square cipher">Four-square</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Great_Cipher" title="Great Cipher">Great</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Hill_cipher" title="Hill cipher">Hill</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Keyword_cipher" title="Keyword cipher">Keyword</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Nihilist_cipher" title="Nihilist cipher">Nihilist</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Permutation_cipher" title="Permutation cipher">Permutation</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Pigpen_cipher" title="Pigpen cipher">Pigpen</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Playfair_cipher" title="Playfair cipher">Playfair</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Polyalphabetic_cipher" title="Polyalphabetic cipher">Polyalphabetic</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Polybius_square" title="Polybius square">Polybius</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Rail_Fence_Cipher" title="Rail Fence Cipher">Rail Fence</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Reihenschieber" title="Reihenschieber">Reihenschieber</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Reservehandverfahren" title="Reservehandverfahren">Reservehandverfahren</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/ROT13" title="ROT13">ROT13</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Running_key_cipher" title="Running key cipher">Running key</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Scytale" title="Scytale">Scytale</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Smithy_code" title="Smithy code">Smithy code</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Solitaire_%28cipher%29" title="Solitaire (cipher)">Solitaire</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Straddling_checkerboard" title="Straddling checkerboard">Straddling checkerboard</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Substitution_cipher" title="Substitution cipher">Substitution</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Tap_Code" title="Tap Code" class="mw-redirect">Tap Code</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Transposition_cipher" title="Transposition cipher">Transposition</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Trifid_cipher" title="Trifid cipher">Trifid</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Two-square_cipher" title="Two-square cipher">Two-square</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/VIC_cipher" title="VIC cipher">VIC cipher</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" title="Vigenère cipher">Vigenère</a></span></p>
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<p><span style="white-space: nowrap;"><b>Cryptanalysis:</b> <a href="http://en.wikipedia.org/wiki/Frequency_analysis" title="Frequency analysis">Frequency analysis</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Index_of_coincidence" title="Index of coincidence">Index of coincidence</a>&nbsp;|</span> <span style="white-space: nowrap;"><strong class="selflink">Kasiski examination</strong></span></p>
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<div style="padding: 0em 0.25em;">
<p><span style="white-space: nowrap;"><b>Misc:</b> <a href="http://en.wikipedia.org/wiki/Cryptogram" title="Cryptogram">Cryptogram</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Bacon%27s_cipher" title="Bacon's cipher">Bacon</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Scytale" title="Scytale">Scytale</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Straddling_checkerboard" title="Straddling checkerboard">Straddling checkerboard</a>&nbsp;|</span> <span style="white-space: nowrap;"><a href="http://en.wikipedia.org/wiki/Tabula_recta" title="Tabula recta">Tabula recta</a></span></p>
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<span style="font-size: 100%;"><a href="http://en.wikipedia.org/wiki/Cryptography" title="Cryptography">Cryptography</a></span></th>
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<div style="padding: 0em 0.25em;"><a href="http://en.wikipedia.org/wiki/History_of_cryptography" title="History of cryptography">History of cryptography</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Cryptanalysis" title="Cryptanalysis">Cryptanalysis</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Portal:Cryptography" title="Portal:Cryptography">Cryptography portal</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Topics_in_cryptography" title="Topics in cryptography">Topics in cryptography</a></div>
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<div style="padding: 0em 0.25em;"><a href="http://en.wikipedia.org/wiki/Symmetric-key_algorithm" title="Symmetric-key algorithm">Symmetric-key algorithm</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Block_cipher" title="Block cipher">Block cipher</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Stream_cipher" title="Stream cipher">Stream cipher</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Message_authentication_code" title="Message authentication code">Message authentication code</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Random numbers</a><span style="font-weight: bold;">&nbsp;·</span> <a href="http://en.wikipedia.org/wiki/Steganography" title="Steganography">Steganography</a></div>
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